The invention relates to electrically small supergain endfire transmitting and receiving resonant antenna arrays with near optimal endfire gains of at least about 7 dB. The difficulties of narrow tolerances, large mismatches, low radiation efficiencies, and reduced scattering of electrically small parasitic elements are overcome by using electrically small resonant antennas as the elements in both separately driven and singly driven (parasitic) two-element (or more) electrically small supergain endfire arrays. Although rapidly increasing narrow tolerances prevent the practical realization of the maximum theoretically possible endfire gain of electrically small arrays with many elements, the theory, numerical simulations, and measurements indicate that near maximum supergains are achievable for electrically small arrays with two and possibly more resonant elements where the decreasing bandwidth with increasing number of elements can be tolerated.
In his 1947 paper on the fundamental limitations of small antennas, Wheeler (H. A. Wheeler, “Fundamental limitations of small antennas,” Proc. IRE, vol. 35, pp. 1479-1484, December 1947) defined a small antenna as “one whose maximum dimension is less than the ‘radian-length’ [λ/(2π)],” where λ is the free-space wavelength. All references in the present specification are herein incorporated by reference.
If one takes a radius a of a sphere that circumscribes an antenna as its “maximum dimension” measured from its center, then an antenna is electrically small if ka<1.0, where k=2π/λ and denotes the free-space wave number. Wheeler defined a small antenna as one with ka≦1.0. S. R. Best in “On the performance properties of the Koch fractal and other bent wire monopoles,” IEEE Trans. Antennas Propagat., vol. 51, pp. 1292-1300, June 2003 (Best) suggests the definition of a small antenna as ka<0.5 based on how small a number of different open-ended, bent-wire antennas have to become for their radiation resistances to be approximately equal.
Here the less stringent criterion if ka<1.0 is used as the definition of an electrically small antenna because we are applying this criterion to array antennas with two or more elements. Since Wheeler's 1947 paper, a myriad of different electrically small antennas have been designed for a variety of applications. None of these electrically small antennas have measured gains appreciably greater than the 10 log10(1.5) (about 1.76 dB) directivity of an elementary electric or magnetic dipole.
A gain of N2 is theoretically possible for a collinear array of N isotropics radiators. This represents a remarkable “supergain” compared to the maximum possible gain, N, for isotropic radiators spaced a half wavelength apart. This supergain is attained as the length of the collinear array approaches zero. It may not be feasible to obtain close to this N2 maximum endfire directivity in practice for a large number of elements because the required accuracy in the values of the magnitude and phase of the excitation currents increases very rapidly with the number of array elements N (See N. Yaru, “A note on super-gain antenna arrays,” Proc. IRE, vol 39, pp. 1081-1085, September 1951).
Closely spaced, two-element, half-wavelength dipole Yagi antennas with measured gains as high as 6 to 7 dB are commercially available and two half-wavelength dipoles with equal but opposite currents and spaced about λ/8 or less achieve a gain of about 6 dB. Closely spaced, three-element, meander-line “Yagi-Uda arrays” with about 7.5 dB gain have been designed recently (though not constructed) with element heights of about a quarter wavelength. Closely spaced, three-element, half-wavelength “folded Yagi arrays” with about 7 dB gain have been recently designed and measured. Also, closely spaced, single-feed, three-element patch antennas approximately one wavelength across have been designed that have a few dB of gain at GHz frequencies. We emphasis however that none of these antennas are electrically small because the electrical size (ka) is greater than one. This level of performance has not been achieved for electrically small antennas.
In contrast to these examples of supergain endfire array antennas consisting of two, three, and four closely spaced λ/2 resonant elements, electrically small (ka<1) endfire transmitting antennas with supergains reasonably close to the theoretical maximum (6-7 dB for two element arrays) have eluded practical realization.